Ridgway is the eldest son of Leonard and Mary Ridgway, and has two younger brothers (John and Neil) and one sister (Lyn). Ridgway emigrated to Canada in 1974 and began his football career while attending M.M. Robinson High School in Burlington, Ontario. In 1977, he began his collegiate football career playing in the Mid American Conference with the University of Toledo Rockets.

His most famous kick as a Roughrider was a 35-yard field goal in the dying moments to lift the Roughriders to a 43-40 victory over the Hamilton Tiger-Cats in the 1989 Grey Cup in what was arguably one of the most thrilling Grey Cup games in history. The game was played in the newly opened Toronto SkyDome and brought the province of Saskatchewan only their second Grey Cup victory in the team's long and storied history.

Ridgway is considered one of the best placekickers to ever play the Canadian game and was known for his dependability in clutch situations. He is one of the most accurate kickers in CFL history for those who have attempted more than 150 career field goals. During his 14-year tenure he attempted 736 field goals and made 574 (78%). He played in 238 games, all with the Roughriders.

In 1987 Ridgway made a then CFL record 60-yard field goal (since surpassed by Paul McCallum in 2001 when he hit from 62 yards; it was the first time in CFL history a field goal was made from that distance). He still holds or shares a number of CFL records such as 59 field goals made in a season in 1990, and 8 field goals made in a game (which he did twice, in 1984 & 1988). Ridgway held the record for most consecutive field goals made, with 28 in 1993. This record—particularly impressive because the majority of his kicks were attempted in the windy confines of Taylor Field—was also bested by McCallum who connected on 30 straight field goals in 2011. Both Ridgway's and McCallum's streaks ended with misses in BC Place Stadium.

His nickname was "Robokicker". and it also the title of his best selling autobiography, Robokicker: An Odyssey through the CFL, which was co-written with David A. Poulsen and published in 1995.

His jersey number 36 is one of only eight jerseys retired by the Roughrider organization. Ridgway was inducted into the Roughriders Plaza of Honour in 2000 and the Canadian Football Hall of Fame in 2003.